Reproducing and extending Brownian motion in optical traps: a computational reimplementation of Volpe and Volpe (2013)

We present an independent computational reimplementation of the model for Brownian motion in an optical trap, originally introduced by Volpe and Volpe (Am J Phys 81(3):224–230, 2013). Using an Euler–Maruyama finite difference scheme to integrate the Langevin equation in Python, we successfully reproduce key results including the transition from ballistic to diffusive motion, optical confinement, and velocity autocorrelation decay. Our implementation provides a quantitative validation of the original work. Furthermore, we extend the analysis to include rotational forces (Grier in Nature 424:810–816, 2003), Kramers transitions in a double-well potential (Hänggi et al. in Rev Mod Phys 62(2):251–341, 1990), and stochastic resonance. This study serves as a transparent, pedagogical resource, providing full code and a critical discussion on numerical methods for stochastic dynamics in computational physics education. The core trade-off of our chosen method clarity and simplicity versus the higher accuracy of advanced integrators is explicitly addressed.